图书简介
The building of conceptual models is an inherent part of our interaction with the world, and the foundation of scientific investigation. Scientists often perform the processes of modelling subconsciously, unaware of the scope and significance of this activity, and the techniques available to assist in the description and testing of their ideas. Mathematics has three important contributions to make in biological modelling: (1) it provides unambiguous languages for expressing relationships at both qualitative and quantitative levels of observation; (2) it allows effective analysis and prediction of model behaviour, and can thereby organize experimental effort productively; (3) it offers rigorous methods of testing hypotheses by comparing models with experimental data; by providing a means of objectively excluding unsuitable concepts, the development of ideas is given a sound experimental basis. Many modern mathematical techniques can be exploited only with the aid of computers. These machines not only provide increased speed and accuracy in determining the consequences of model assumptions, but also greatly extend the range of problems which can be explored. The impact of computers in the biological sciences has been widespread and revolutionary, and will continue to be so.
1 Modelling in Biology.- 1.1 The Nature of Scientific Models.- 1.2 Clarity from Complexity.- 1.3 Experimental Data.- 1.4 Predictions from Models — Simulation.- 1.5 A Model of Complexity Producing Organized Simplicity.- 1.6 Subjectivity in Modelling.- 1.7 Mathematics in Modelling.- 1.8 Computers and Models.- 1.9 Description of Models.- 1.10 Modelling in Perspective.- 1.11 Advantages in Modelling.- 2 Mathematical Descriptions of Biological Models.- 2.1 Theoretical Modelling — Analysis of Mechanism.- 2.2 Linearity and Non-Linearity.- 2.3 Empirical Modelling — a Description of System Response.- 2.4 Point Stability in Models.- 2.5 Concepts of Feedback.- 2.6 Biological Development and Mathematics Beyond Instability.- 2.7 Finite Level Modelling.- 2.8 The Need for Statistics.- 3 Comparing Models with Experimental Results.- 3.1 Analogue Simulation.- 3.2 Approximate Simulation by Digital Computer.- 3.3 Suitable Digital Computers.- 3.4 Estimation of Parameters.- 3.5 Practical Details of Fitting Non-Linear Models to Data.- 3.6 Models Containing Differential Equations.- 3.7 Using the Computer to Fit Models to Data.- 4 Design of Analytical Experiments.- 4.1 Principles of Design.- 4.2 Sequential Design.- 5 Dynamic Systems: Clearance and Compartmental Analysis.- 5.1 Clearance.- 5.2 Compartmental Analysis.- 6 Ligand—Protein Interaction and Competitive Displacement Assays.- 6.1 Interactions Between Ligands and Macromolecules.- 6.2 Competitive Protein-Binding Assays.- 7 Mathematical Modelling of Biological Rhythms.- 7.1 Biological Rhythms: Experimental Evidence.- 7.2 The Contribution of Mathematics.- 7.3 Response of Rhythms to Stimuli — Rhythm Coupling.- 7.4 Rhythms, Endocrinology and Biological Control.- 7.5 Empirical Characterization of Rhythms from Data.- 8 Large Systems: Modelling Ovulatory Cycles.- 8.1 Modelling the Ovulatory Cycle.- 8.2 A Description of the Ovulatory Cycle.- 8.3 Use of Differential Equations with Cyclic Solutions.- 8.4 Use of a Threshold Discontinuity to Produce Cyclicity.- 8.5 A Physiologically Based Model of the Rat Oestrous Cycle.- 8.6 An Empirical Model of the Rat Oestrous Cycle Controlled by Time.- 8.7 An Attempt to Include More Variables.- 8.8 Eliminating the Differential Equations: A Finite Level Model.- 8.9 A “Complete” Description.- 8.10 Conclusions.- 9 Stochastic Models.- 9.1 Non-Parametric Statistical Models.- 9.2 Multivariate Analysis.- 10 Appendix A: A Summary of Relevant Statistics.- 10.1 Variance, Standard Deviation and Weight.- 10.2 The Propagation of Variance.- 10.3 Covariance and Correlation.- 10.4 z-Scores, or Standardized Measures.- 10.5 Testing Hypotheses.- 10.6 Runs-Test.- 10.7 Chi-Square Test.- 10.8 Tests of Normality of Distribution.- 10.9 Comparing Two Parameters: The r-Test.- 10.10 Comparing Any Number of Parameters: Analysis of Variance.- 10.11 The Variance Ratio or F-Test.- 10.12 Confidence Intervals.- 10.13 Control Charts.- 11 Appendix B: Computer Programs.- 11.1 MODFIT: A General Model-Fitting Program.- 11.2 SIMUL: A Program for Monte Carlo Simulation.- 11.3 FUNCTN Subprogram RESERVR: Exponential Decay.- 11.4 FUNCTN Subprogram EXPCUBE: Growth of Organisms.- 11.5 FUNCTN Subprogram POLYNOM: General Polynomial.- 11.6 FUNCTN Subprogram FOLL: Growth of Ovarian Follicles.- 11.7 DESIGN: A Program for Efficient Experimental Design.- 11.8 FUNCTN Subprogram CAI: Compartmental Analysis.- 11.9 FUNCTN Subprogram CA2: Compartmental Analysis.- 11.10 FUNCTN Subprogram CA2A: Compartmental Analysis.- 11.11 FUNCTN Subprogram CA3: Compartmental Analysis.- 11.12 FUNCTN Subprogram MASSACT: Ligand Binding.- 11.13 FUNCTN Subprogram GENBIND: Ligand Binding.- 11.14 FUNCTN Subprogram RIA: Competitive Protein-Binding.- 11.15 FUNCTN Subprogram RIAH: Competitive Protein-Binding.- 11.16 FUNCTN Subprogram SIN: Rhythmical Data.- 11.17 FUNCTN Subprogram LIMIT: Limit Cycles.- 11.18 Other Programs for Fitting Non-Linear Models to
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